# Problem 009

A Pythagorean triplet is a set of three natural numbers, a < b < c, for which, a^(2) + b^(2) = c^(2) For example, 3^(2) + 4^(2) = 9 + 16 = 25 = 5^(2). There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc.

Solution:
```Function Prob009() As Long For a As Integer = 0 To 1000 For b As Integer = 0 To 1000 For c As Integer = 0 To 1000 If (a + b + c) = 1000 AndAlso a < b AndAlso b < c AndAlso System.Math.Pow(a, 2) + System.Math.Pow(b, 2) = System.Math.Pow(c, 2) Then Return a * b * c Next Next Next End Function```

Summary:
Pretty easy...

# Problem 008

Find the greatest product of five consecutive digits in the 1000-digit number.

73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450

Solution:
```Function Prob008() As Long Dim strInput As New System.Text.StringBuilder strInput.Append("73167176531330624919225119674426574742355349194934") strInput.Append("96983520312774506326239578318016984801869478851843") strInput.Append("85861560789112949495459501737958331952853208805511") strInput.Append("12540698747158523863050715693290963295227443043557") strInput.Append("66896648950445244523161731856403098711121722383113") strInput.Append("62229893423380308135336276614282806444486645238749") strInput.Append("30358907296290491560440772390713810515859307960866") strInput.Append("70172427121883998797908792274921901699720888093776") strInput.Append("65727333001053367881220235421809751254540594752243") strInput.Append("52584907711670556013604839586446706324415722155397") strInput.Append("53697817977846174064955149290862569321978468622482") strInput.Append("83972241375657056057490261407972968652414535100474") strInput.Append("82166370484403199890008895243450658541227588666881") strInput.Append("16427171479924442928230863465674813919123162824586") strInput.Append("17866458359124566529476545682848912883142607690042") strInput.Append("24219022671055626321111109370544217506941658960408") strInput.Append("07198403850962455444362981230987879927244284909188") strInput.Append("84580156166097919133875499200524063689912560717606") strInput.Append("05886116467109405077541002256983155200055935729725") strInput.Append("71636269561882670428252483600823257530420752963450") Dim Group1 As Integer = 0 Dim Group2 As Integer = 0 Dim Group3 As Integer = 0 Dim Group4 As Integer = 0 Dim Group5 As Integer = 0 Dim StringPos As Integer = 0 Do While StringPos < strInput.Length - 4 Group1 = strInput.ToString.Substring(StringPos, 1) Group2 = strInput.ToString.Substring(StringPos + 1, 1) Group3 = strInput.ToString.Substring(StringPos + 2, 1) Group4 = strInput.ToString.Substring(StringPos + 3, 1) Group5 = strInput.ToString.Substring(StringPos + 4, 1) If Group1 * Group2 * Group3 * Group4 * Group5 > Prob008 Then Prob008 = Group1 * Group2 * Group3 * Group4 * Group5 StringPos += 1 Loop End Function```

Summary:
It isn’t pretty, but it works :)

# Problem 007

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6^(th) prime is 13.

What is the 10001^(st) prime number?

Solution:
```Function Prob007() As Long Dim k As Integer = 1 Dim PrimeCount As Integer = 0 Dim TargetPrime As Integer = 10001 While PrimeCount < = TargetPrime k += 1 If IsPrime(k) Then PrimeCount += 1 If PrimeCount = TargetPrime Then Return k End While End Function```

Summary:
Simple and gets the job done.

# Problem 006

The sum of the squares of the first ten natural numbers is,
1^(2) + 2^(2) + … + 10^(2) = 385

The square of the sum of the first ten natural numbers is,
(1 + 2 + … + 10)^(2) = 55^(2) = 3025

Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 − 385 = 2640.

Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

Solution:
```Function Prob006() As Long Dim SumOfSquares As Long = 0 For k As Integer = 1 To 100 SumOfSquares += System.Math.Pow(k, 2) Next Dim Sum As Long = 0 For k As Integer = 1 To 100 Sum += k Next Dim SquareOfSum As Long = System.Math.Pow(Sum, 2) Return SquareOfSum - SumOfSquares End Function```

Summary:

# Problem 005

2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.

What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?

Solution:
```Function Prob005() As Integer Dim FoundResult As Boolean = False Dim k As Integer = 0 While FoundResult = False k += 1 FoundResult = True For f As Integer = 1 To 20 If k Mod f <> 0 Then FoundResult = False End If Next If FoundResult = True Then Return k End While End Function```

Summary:
This was pretty easy, but it seems like the problems are building upon each other, so I’m sure the next few are going to be a major pain…